A Possible Mechanism for the Formation of Hurricane Rainbands

Abstract

In a model of hurricane rainbands as linear waves on a barotropic mean vortex, it is possible to derive two conservation laws for the perturbations: both the azimuthally integrated Reynolds torque exerted by the waves and the ratio of the azimuthally integrated radial wave energy flux to the intrinsic frequency are constant with radius for a steady wave field without dissipation or cumulus heating. The latter of these conditions can be invoked to explain the amplification of a class of waves that sustains a flux of energy directed into the vortex center and one of angular momentum directed out of it. The intrinsic phase propagation in the tangential direction is against the mean flow, but it is not fast enough to prevent the waves from being advected slowly downwind in the cyclonic sense. The Doppler shift leads to an increase in the intrinsic frequency toward the center and, in consequence of the second conservation law, to an amplification of the wave energy flux, as well as a large increase in the wave amplitude. For a sufficiently intense mean vortex, the waves are absorbed in the eye wall when their intrinsic frequency reaches the buoyancy frequency. If the initial frequency at the storm's periphery is near the inertia frequency, the maximum possible amplification of the energy flux is then slightly less than the ratio of the buoyancy frequency to the Coriolis frequency.